On the accuracy of the mortar finite volume element method with Lagrange multipliers
type: Item
instance of: scholarly article
title: On the accuracy of the mortar finite volume element method with Lagrange multipliers
zbMATH Open document ID: 1120.65123
author: Yufei Cao
author: Hongxing Rui
published in: Applied Mathematics and Computation
publication date: 2007-02-19T00:00:00Z
review text: The authors consider the following elliptic boundary value problem \[ \begin{aligned} -\nabla\cdot(A\nabla u) = f \quad & \quad \text{in }\Omega, \\ u = 0 \quad & \quad \text{on }\partial\Omega, \end{aligned} \] where \(\Omega\subset \mathbb{R}^{2}\) is a bounded convex polygonal domain with boundary \(\partial\Omega\), \(A=(a_{ij}(x))_{2\times 2}\) is a given symmetric and uniformly positive definite matrix in \(\Omega\), \(a_{ij}\in C^{1}(\overline{\Omega})\), \(1\leq i,j\leq 2\), and the source term \(f = f(x)\) is regular enough such that the problem has a unique solution in a certain Sobolev space. The authors investigate the accuracy of the mortar finite volume element (MFVE) method for the problem stated above. They consider the MFVE scheme which follows the traditional mortar approach and use finite volume element approximations only in the subdomains and finite element in the interfaces for Lagrange multipliers. The authors extend the \(H^{1}\)-norm error estimate of \textit{R. Ewing, R. Lazarov, T. Lin}, and \textit{Y. Lin} [East-West J. Numer. Math. 8, No. 2, 93--110 (2000; Zbl 0963.65112)] and prove the general \(L^{2}\)-norm error estimate to show how the regularity of the source term \(f\) can affect the convergence rate of the MFVE solution. Finally, the uniform convergence of the solution for the MFVE method under minimal regularity assumption is presented.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 5128324
zbMATH Keywords: error estimates
zbMATH Keywords: minimal regularity
zbMATH Keywords: elliptic boundary value problem
zbMATH Keywords: mortar finite volume element (MFVE) method
zbMATH Keywords: uniform convergence
reviewed by: Petr Necesal
MaRDI profile type: Publication
full work available at URL: j.amc.2006.05.142
OpenAlex ID: W2061601676
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DOI: 10.1016/J.AMC.2006.05.142
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description: scientific article; zbMATH DE number 5128324